In the product, multiplying the first factor by \(10\) and dividing the second by \(10\) leaves the total factor unchanged.

In the division claim, the numerator becomes ten times larger while the divisor becomes ten times smaller. Each change makes the quotient ten times larger, so together they make it \(100\) times larger.

To keep the quotient unchanged, multiply both numerator and denominator by \(10\): \(\displaystyle \frac{0.6}{350}=\frac{6}{3500}\).

Answer

The correct division is \(0.6\div350=6\div3500\). The claimed quotient \(6\div35\) is \(100\) times the original.